The present invention relates to trimming materials, and in particular to a constraint based paper reel trimming controller.
Planning production and distribution of paper products in real world manufacturing environments is an extremely complex task. Hundreds of constraints and business objectives need to be considered. In the paper and pulp industry, planning is required for trimming huge paper rolls into different width, based on requirements and machine constraints.
In operation, a paper machine produces large rolls of paper, called reels. The width of the reel is referred to as the deckle, and is normally fixed for each machine. Another machine, referred to as the winder, cuts the reels into rolls of smaller diameter and width. The process of trimming a reel to make rolls is called trimming.
Several sets of rolls are made from each reel. The widths and diameter of these rolls must match customer requirements as represented by customer orders. Sometimes a manufacturer may produce more or less (within specified tolerance) than an ordered amount. The amount produced in excess of the order quantity is a called overrun. Production shortfalls are called underruns.
Trimming is a classical combinatorial optimization problem, which finds out how to combine various customer orders on a winder machine of the same product type to achieve certain objectives, such as minimization of wastage and limiting the amount of overrun and underrun. A pattern for trimming is simply a combination of different roll widths that sum up to a given deckle size. Selecting the pattern for trimming is typically an integer programming problem. The number of variables used is proportional to the number of orders. As a result, it is computationally intensive. An alternative way to provide solutions is to use dynamic column generation and relaxation methods.
A pattern solution set for material trimming to fulfill orders is generated using constraint programming and a heuristic. In one embodiment, the material comprises a paper reel that is to be divided into different width rolls. For every pattern generated, an objective function is evaluated based on the sum of waste factor and the variance of the quantity ordered for all widths in that pattern. The pattern that has the least objective function is chosen with the maximum number of sets possible. Orders are updated with the quantities left over and then the process continues, forming a solution tree, which serves as an initial solution set.
In one embodiment, the initial solution set is checked individually against the average loss of the solution set. Nodes in the solution tree having trim loss greater than the average loss are identified. Branches of the tree emanating from its parent are explored for better patterns considering overrun/underrun tolerances given by the customer for orders to yield multiple solutions. The process continues until all patterns are below the initial average loss.